Category Theory with Applications in Functional Programming: Ph.D. Course

Third Day Programme

The third day in the course takes place Wednesday 21 October from 9:00 to 15:00 at SLV300-0.2.13

The programme for the third day of the course is as follows:

9:00CT3.1: Constructions in categories: Products, equalizers, limits, co-limits; Cartesian closed categories
9:40Break
9:50CT3.2: Adjoints preserve limits; Example: categorical constructions for transition systems
10:40Exercises
11:20CT3.3: Example: Solutions to recursive domain equations
12:00Lunch
12:30FP3
15:00Closing

Reading

The new Mac Lane sections are available on-line here; for the Smyth-Plotkin and Rosendahl articles see the home page.

Pierce 3.4, Smyth-Plotkin (Solution), and Rosendahl (Domæneteori) all cover our example on solutions to recursive domain equations. None of them is 100% suited for our purpose, so we will pick some stuff from all three. Rosendahl in particular is good for motivation, hence easy to read before the lecture, but not very categorical.

Exercises

  1. Pierce 1.4.6.2
  2. Pierce 1.5.6.4
  3. Pierce 1.7.4.1
  4. Pierce 1.8.7.2. Also dualize to pushouts and epis
  5. Pierce 1.9.10.2
  6. Pierce 1.10.5.5, 1.10.5.6
  7. Mac Lane 3.3.4, 3.3.5 (p.68)
  8. Mac Lane 3.4.4 (p.72). Also dualize to monos and pushouts
  9. Mac Lane 3.4.8 (p.72)
  10. Mac Lane 4.6.4 (p.98)
  11. Rosendahl 6.1, 6.2

Slides etc.